If is defined on the domain

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If f(x)f(x) is defined on the domain [0,1][0,1], then f(2sin⁡x)f(2\sin x) is defined on (a) ⋃n∈I([2nπ,2nπ+π6]∪[2nπ+5π6,(2n+1)π])\bigcup_{n\in I}\left(\left[2n\pi,2n\pi+\frac{\pi}{6}\right]\cup\left[2n\pi+\frac{5\pi}{6},(2n+1)\pi\right]\right) (b) ⋃n∈I[2nπ,2nπ+π6]\bigcup_{n\in I}\left[2n\pi,2n\pi+\frac{\pi}{6}\right] (c) ⋃n∈I[2nπ+5π6,(2n+1)π]\bigcup_{n\in I}\left[2n\pi+\frac{5\pi}{6},(2n+1)\pi\right] (d) None of these

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